You are axo-facto right, Bill.
I guess I was spoiled by mostly doing sound for my band, where I had total 'dictator-like control' over sound.
I mean, it
can be done right, and like you say, most small clubs do it that way. I've heard a FEW (rare) cases where it worked.
But holy shit, the louder the system, the less you need it for 'reinforcement' and more for total sound projection!